## Success Stories

### SENIOR MATH MAJOR EARNS TOP 25 NATIONAL RANKING

Isaac Hellerman, a senior mathematics major, has placed in the top 25 on the national
Putnam exam, a mathematics competition for undergraduates. This prestigious contest
is now in its 83rd year, and it challenges undergraduates to solve 12 problems over
the course of six hours. Isaac scored a remarkable 77 points (out of 120) on this
year’s exam, which earned him 17 th place nationally. Furthermore, the only other
schools with participants ranking in the top 25 were MIT, Harvard, Stanford, and Yale.
This is the first time that a student from the University of Dallas has placed in
the top 25.

Overall, the University of Dallas had seven participants compete in the Putnam Competition
this year: seniors Isaac Hellerman and Phoebe Jones; juniors Lauren Engelthaler, Teresa
Gulding, and James Latour; sophomore Kate Brady; and freshman Kilty Edwards. The top
three scores were used to rank the team from the University of Dallas, which earned
them a national rank of 37th overall, a university record on the Putnam.

Thousands of participants from the United States and Canada compete each year, earning
both individual and team prizes. All participants whose score is in the top 25 earn
cash prizes ranging from

$2500 to $250. This year, 3,415 students at 456 institutions participated in the competition.
Each problem is scored out of 10 points, and the exam is so challenging that the median
score each year is

either 0 or 1 points out of the possible 120 points. Below is a sample problem from
this year’s Putnam, which only 81 participants solved, including Isaac.

**B4 ** Find all integers *n* with *n*≥*4* for which there exists a sequence of distinct real numbers {x_{1}, … ,x_{n}} such that each of the sets {x_{1},x_{2},x_{3}}, {x_{2},x_{3},x_{4}}, … ,{x_{n-2},x_{n-1},x_{n}}, {x_{n-1},x_{n},x_{1}}, {x_{n},x_{1}x_{2}} forms a 3-term arithmetic progression when arranged in increasing order.

### UD Students Earn Meritorious Designation

For only the second time, a team from UD, consisting of juniors Therese Aglialoro,
William Kostuch, and Cameron Nottingham, has been awarded the designation **Meritorious** in the international Mathematical Contest in Modeling (MCM). Such a designation
places them in the top 8% of all teams, with a total 13,749 teams participating in
this year’s MCM. Furthermore, the UD team was the only team in the United States
to achieve the designation Meritorious or higher on their particular problem and one
of only 18 teams nationally on any of the MCM problems posed.

The contest challenges teams to clarify, analyze, and propose a solution to their choice of one of three open-ended, real-world problems. Teams develop and apply mathematical models to solve their chosen problem and may use any resource available, such as websites, books and articles, computers, and databases. Each team has exactly four days to solve their problem and write a 20-page solution paper that communicates their approach and results. Teams are awarded one of five designations: Successful Participant, Honorable Mention, Meritorious, Finalist, and Outstanding. The last time UD earned the meritorious designation was in 1995 by the team of Rebecca Beasley, Daniel Dauenhauer, and Brian Klingle.

The problem that Agialoro, Kostuch, and Nottingham chose required teams to construct a mathematical model to identify the best 3-dimensional geometric shape to use as a sandcastle foundation that will last the longest period of time on a seashore that experiences waves and tides. Part of the required analysis included determining an optimal sand-to-water mixture proportion for the castle foundation. In addition, teams had to determine if their foundation remains the best 3-dimensional geometric shape when it is raining. Finally, teams had to write a 2-page non-technical summary suitable for publication in a fictitious vacation magazine.

In their paper titled, “The Best Sandcastles Are Egyptian: Pyramids Reign Supreme,” Aglialoro, Kostuch, and Nottingham identified the best water-to-sand ratio to be around 6% by adapting known results on granular cohesion to their scenario. They then wrote and implemented a computer model that tested sandcastle strength, checking for collapse due to shear stress, erosion, and oversaturation. After applying their model to cubes, cylinders, pyramids, and cones, they determined that the shape that withstood waves and tides best was the pyramid, even when rain was included as a possible factor.

Dr. John Osoinach has served as faculty advisor for UD teams for the past six years, having advised nine teams so far. He praised this team’s ingenuity and hard work on their solution, remarking that “their sandcastle paper will be used as a guide for future UD teams. It’s an exceptionally well-written paper that uses mathematics in both practical and creative ways.” Dr. Osoinach looks forward to advising other teams in the future, saying “UD students are very well suited for this contest, as it’s as much about clear writing as it is about mathematical modeling.”

### UD’s First Recipient of the Trjitzinsky Memorial Award

Date Published: Nov. 27, 2017

Sophomore **Mary Kate Tomassi**, BA ’20, “embodies the diligent student who loves learning mathematics,” explained
Assistant Professor of Mathematics John Osoinach, as faculty and students gathered
in Constantin Garden on Wednesday, Nov. 15, to honor Tomassi’s achievement as UD’s
first recipient of the Waldemar J. Trjitzinsky Memorial Award.

As one of seven undergraduates to receive this year’s award given by the American Mathematical Society (AMS), Tomassi will delve further into the field of mathematics in her studies at UD, as well as explore her interest in computer science. UD was one of seven schools in the country selected by the AMS to bestow the award on one worthy student who plans on pursuing a career in mathematics.

“There are plenty of deserving math students at UD,” said Tomassi. “I’m honored to receive such an award, and I’m especially grateful for the support of my professors in the Mathematics Department.”

Although still undecided where her career in mathematics will take her after UD, Tomassi would like to make a positive impact in society by working on issues such as homelessness or human trafficking. “Mathematics allows you to explore and work in so many different disciplines,” she said.

“I truly enjoy studying mathematics, because it gives you an opportunity to further explore philosophical thought in a more tangible sense,” she said. “Learning about the process of mathematics has helped me form better methods of decision making and critical thinking, which benefit not only my studies at UD but my day-to-day life.”

According to her award biography, “Mary Kate is one of those rare students who not only excels in mathematics, but also embraces the mathematics culture at the university by working in the Mathematics Department office.”

Additionally, Texas Right to Life named Tomassi one of 38 2017 Dr. Joseph Graham College Fellows in April. Over the summer, she participated in a week-long training program as part of this fellowship to gain pro-life knowledge and leadership skills to bring back to UD.

This year celebrates the 25th anniversary of the establishment of the Waldemar J. Trjitzinsky Memorial Awards, which was made possible by a bequest from the estate of Waldemar J., Barbara G. and Juliette Trjitzinsky. These funds help support mathematics students who lack financial resources. Each year the society selects a number of geographically distributed schools who in turn make one-time awards to assist students in pursuit of mathematics careers.

### Team Places 55th in National Math Contest

**Problem B3:**Let

*A*be an

*m*by

*n*matrix with rational entries. Suppose that there are at least

*m + n*distinct prime numbers among the absolute values of the entries of

*A*. Show that the rank of

*A*is at least

*2*.

### "UD math students delve deeper..."

### UD Mathematics Department Number One in Percentage of BA's to Later Earn Ph.D's

###

Math Major Wins Award at Conference

In April of 2013, senior mathematics major Hoai-Ngoc Ngo presented her research in Biomathematics at the 93rd annual Texas section meeting of the Mathematical Association of America. The conference drew faculty and students from across the state, contributing 100 talks in total, nearly half of which were by undergraduates presenting their research. For her talk titled, Diversity and Homogeneity Revealed in SSR Analyses of NCGR Cultivars, Ngoc received first prize for the depth of her research as well as her exceptional presentation. In her research, Ngoc applied both statistical techniques and vector analysis to the problem of determining the genetic fingerprints of cranberry cultivars. Since previous crosses of cranberry cultivars have produced advantageous offspring, the goal of this research was to assist in the process of developing new and desirable cranberry cultivars. Using her statistical and mathematical techniques, Ngoc was able to find many discrepancies within previously identified cultivars, and consequently she was able to demonstrate the need to change the approach used to determine the pedigrees of these cultivars.